The invention concerns a cryogenic process of simultaneous selective desulphuration and gasoline removal of a gaseous mixture consisting mainly of methane and likewise containing H.sub.2 S, hydrocarbons with C.sub.2 and more, and eventually one or more gaseous compounds selected among the inert gases H.sub.2 O, CO.sub.2, COS and mercaptans, said gaseous mixture being under an absolute pressure above 0.5 MPa. The process according to the invention makes it possible directly to separate a gaseous mixture of the above mentioned type in three components, namely:
a treated gas mainly consisting of methane in which the partial pressure H.sub.2 S is less than 65 Pa and the total partial pressure of sulphur-containing compounds, when the gaseous mixture to be treated contains COS and/or mercaptans in addition to H.sub.2 S, is less than 260 Pa, PA1 one fraction of heavy hydrocarbons containing at least 80% molar of hydrocarbons of C.sub.3 and more present in the gaseous mixture to be treated, and PA1 one stream of acid gas consisting of H.sub.2 S eventually mixed with a more or less considerable quantity of acid compounds CO.sub.2, COS and mercaptans, when said compounds are present in the gaseous mixture to be treated, said stream of acid gas containing, one the one hand, less than 5% molar of hydrocarbons expressed in methane equivalent in relation to the H.sub.2 S and other acid compounds and more than 80% of the H.sub.2 S contained in the gaseous mixture to be treated, and, on the other hand, having a molar ratio H.sub.2 S:CO.sub.2 higher than the ratio that corresponds in the gaseous mixtures to be treated.